Hölder continuity of three types of generalized synchronization manifolds of non-autonomous systems |
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| Institution: | 1. School of Science, Jiangnan University, Wuxi 214122, China;2. School of Information Technology, Jiangnan University, Wuxi 214122, China;1. Department of Neurology, The First Affiliated Hospital, Chongqing Medical University, Chongqing, China;2. Institute of Neuroscience and the Collaborative Innovation Center for Brain Science, Chongqing Medical University, Chongqing, China;3. Chongqing Key Laboratory of Neurobiology, Chongqing, China;4. Department of Neurology, Yongchuan Hospital, Chongqing Medical University, Chongqing, China;1. Institute of Psychology, University of Tartu, Näituse 2, Tartu 50409, Estonia;2. Institute of Public Law, University of Tartu, Teatri väljak 3-207, Tallinn 10143, Estonia;3. Institute of Computer Science, University of Tartu, J. Liivi 2, Tartu 50409, Estonia;1. Department of Sports Medicine, China Medical University, Shenyang 110122, PR China;2. Department of Human Anatomy, China Medical University, Shenyang 110122, PR China;1. Department of Neurology, The Second Hospital of Hebei Medical University, Shijiazhuang, China;2. Key Laboratory of Hebei Neurology, Shijiazhuang, China;3. Hebei Institute of Cardiocerebrovascular Disease, Shijiazhuang, China |
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| Abstract: | This paper studies the existence of Hölder continuity of the generalized synchronization (GS) manifold. When the modified response system has an asymptotically stable equilibrium, periodic or quasi-periodic orbit, and chaotic attractor, GS is classified into four types accordingly. The first three types of GS are considered, and based on the Schauder fixed point theorem, sufficient conditions for Hölder continuous GS in the coupled non-autonomous systems are derived and theoretically proved. |
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